Chief Superintendent Mark Sutherland, Police Scotland's Divisional Commander for Greater Glasgow, said: "Today is understandably a significant day for Rangers Football Club and its supporters.
"We understand the importance of football in Glasgow, how it connects our communities and, is for many, a culture and a way of life.
“We are however still in the midst of a pandemic and under Coronavirus restrictions people should not be gathering for any reason.
"The overarching aim of Police Scotland's operation today remains public safety.
"Throughout the day we have seen crowds gather and anti-social behaviour including the use of pyrotechnics and drinking in public.
"Our officers are dealing with such offences where possible and have made arrests."
On Friday, the First Minister announced that the city of Glasgow as well as Moray would have to remain in level three due to a high number of coronavirus cases.
The rest of mainland Scotland will enter level two on Monday.
Concerns were raised about the fans response to the cup presentation to Rangers with Police Scotland and the Scottish Government issuing prior warnings to act with caution.
Chief Superintendent Sutherland continued: “A request to facilitate a fan procession to Glasgow city centre was declined and officers moved to the procession location to intervene.
"A short time later large crowds gathered at separate locations and began to move off, due to the size of the crowd, the supporters were escorted to George Square to ensure public safety and minimise disruption to the community.
"Given the largely peaceful nature of the crowd, it would not be proportionate for our resources to use a high level of force through public order policing to disperse those gathering.
"We have seen some disruption to traffic, but no long lasting disruption to our communities.
"Like all citizens of Glasgow we remain concerned about public health and the ongoing response to the pandemic, especially given the decision to keep Glasgow in level 3 restrictions.
"The Chief Constable has made it clear that people should take personal responsibility and do the right thing. "